Achieving near-zero τf in garnets via normal-inverse structural transformation in an inverse garnet Mg3Yb2Ge3O12

In this study, garnet-structured Mg 3 Yb 2 Ge 3 O 12 ceramics were synthesized via conventional solid-state reaction. Ceramics sintered at 1430 °C achieved high relative densities (∼98 %) and superior microwave dielectric properties: ε ᵣ = 13.7 ± 0.2, Q × f = 11,424 ± 500 GHz, and a rare positive τ f = +71.6 ± 0.7 ppm/°C. To modulate τ f , inverse-to-normal garnet phase transformation was achieved using a compositional tuning strategy, which led to the formation of a series of Ca x Mg 3- x Yb 2 Ge 3 O 12 . Rietveld refinement of X-ray diffraction patterns confirmed a low-angle shift with increasing x , indicating progressive lattice expansion and unit-cell volume enlargement. With increasing Ca²⁺ content, τ f transitioned from positive to negative values, approaching zero near x  = 0.5, while the overall dielectric performance was enhanced. This strategy provides new pathways for τ f control in A₃B₂C₃O₁₂-structured ceramics.